Theropod rotational inertia

[Infinity Blade]

I wanted to reply a bit to creature's response to what I said in 'Answer with a question', but I also didn't want to hijack the thread. So here's a topic regarding theropod rotational inertia.

Anyway:

Sept 23, 2016 19:19:24 GMT 5 creature386 said:

I think you could point out that what LionClaws referred to as caterpillar motion can be applied to theropods as the second paper you cited compared theropods to snakes ("Theropods were not laterally stiff, and it is likely that most theropods turned with a more serpentine motion – turning first their heads and necks, then torsos, then hips, and finally, in a sinuous motion, their tails") and that the sort of turning he described is more applicable to hippos than theropods.
He did have a point though when saying that not having a problem is better than reducing it.

I don't think I agree with that last statement. I envision a theropod's means of dealing with rotational inertia as akin to a tall person's means of going under a limbo stick. A short (enough) person may be able to just run right under it, but a tall person who can't do this can simply duck under it.

[creature386]

Well, the limbo analogy does show that even this reduction of the problem comes with tradeoffs. Ducking walking takes more effort and time than just walking below it. And I think even the first paper you've shown in response to LionClaws admitted that the inertia problem in theropods is not fully removed. Consider this passage:

We will never know how non-avian theropods utilized tail movements in turning maneuvers, but observations on extant species with large tails should be helpful. When basilisk lizards (Basiliscus basiliscus) execute rapid 90° running turns, they sometimes use the angular momentum of their long tails to produce body rotations of up to 45° (D. R. Carrier, unpublished observations). To produce the desired rotation of the body, they rapidly swing the tail laterally during a brief period of little or no limb support. The recovery swing of the tail always occurs during periods of simultaneous fore- and hindlimb support and often involves some degree of vertical excursion. Although basilisk lizards are renowned for their bipedal running, they are unable to complete 90 ° running turns without adopting a quadrupedal gait (Khan and Carrier, 2000). Hence, because the tail of theropods acted as a gravitational counterweight to the body, vertical recovery swings of the tail, such as those used by basilisk lizards, would probably have disrupted dynamic balance. Thus, we believe tail-swinging would have been of limited utility to bipedal theropods during the execution of sudden and sustained turns.

It is interesting because basilisks have most of the relevant adaptations theropods have (or at least the tail), yet are somewhat more agile during quadrupedal walking.

[Infinity Blade]

Well, the limbo analogy does show that even this reduction of the problem comes with tradeoffs. Ducking walking takes more effort and time than just walking below it.

A lot of that time is shaved off if one acts preemptively to duck beneath. If anything, yes, it takes more effort than to simply run underneath it, but I'm not sure if this matters too much as both would still be such effective means of avoiding collision with the limbo stick.

And I think even the first paper you've shown in response to LionClaws admitted that the inertia problem in theropods is not fully removed. Consider this passage:

We will never know how non-avian theropods utilized tail movements in turning maneuvers, but observations on extant species with large tails should be helpful. When basilisk lizards (Basiliscus basiliscus) execute rapid 90° running turns, they sometimes use the angular momentum of their long tails to produce body rotations of up to 45° (D. R. Carrier, unpublished observations). To produce the desired rotation of the body, they rapidly swing the tail laterally during a brief period of little or no limb support. The recovery swing of the tail always occurs during periods of simultaneous fore- and hindlimb support and often involves some degree of vertical excursion. Although basilisk lizards are renowned for their bipedal running, they are unable to complete 90 ° running turns without adopting a quadrupedal gait (Khan and Carrier, 2000). Hence, because the tail of theropods acted as a gravitational counterweight to the body, vertical recovery swings of the tail, such as those used by basilisk lizards, would probably have disrupted dynamic balance. Thus, we believe tail-swinging would have been of limited utility to bipedal theropods during the execution of sudden and sustained turns.

It is interesting because basilisks have most of the relevant adaptations theropods have (or at least the tail), yet are somewhat more agile during quadrupedal walking.

That might be because, according to The Carnivorous Dinosaurs (Kenneth Carpenter), lizards are unable to sharply turn via banking, as it thinks theropods should have been able to do.

Theropods should have been able to improve maneuverability by leaning into turns the way narrow trackway bicycles and humans do. Wide-track lizards cannot turn sharply by banking, so they must reduce distal inertial mass by erection of the body and tail when running bipedally.

link

I guess when it comes to 90 degree turns, they must turn to a quadrupedal gait.

[Infinity Blade]

I'm dying to hear your thoughts on this theropod.

[theropod]

Hey, sorry it took me so long. I was on a rather long and exhausting field trip to the pyrenees these last two weeks and we got about 2 hours of free time a day, which were pretty much fully occupied with acquiring sufficient nutrition and personal hygiene.

I’m flattered that you are this interested in my opinion, I’ll have a look at carnivora now and get back to you then.

[theropod]

OK, I think I got the gist of your hippo/Carnotaurus discussion, but tell me if I’ve overlooked important points:

First of all, I definitely agree with you about the use of turning in a sinuous motion. In fact I think it’s so blatantly obvious that a theropod would turn like that that it’s very weird that anybody would struggle with the concept or presume turning like a twirling cane as some sort of default.
If an animal wants to face in a certain direction, the first thing it’s going to do is move its head, then neck, torso and so forth. There are two damn good reasons for this, one is that a change of posture is more efficient and quicker than rotating the whole body, so you wanna try that first and only turn completely if you actually have to (which, see below, isn’t necessarily the case if you have such a long body). And the other is that by flexing the body the mass is distributed closer to the center of rotation, and the rotational inertia decreases, so in case you do have to turn, you can do it more quickly.

And due to their long, flexible neck and torso (compared to most quadrupeds and the majority of large predators) theropods are certainly not the exception here. Ergo, if a theropod wanted to turn, say, 90 degrees to the side in order to apprehend a prey item, prevent being outflanked, or change direction while running, obviously it would use the whole motion of its torso to achieve the turn, which should make it faster and more efficient in every case, vastly so in some cases, especially when trying to prevent being outflanked.
Carnotaurus has more than twice the epaxial muscle mass of a hippo for a given size (Mazzetta 1998) so I’d assume it would not just leave those muscle. The hippo is making use of its axial muscles too after all, so it’s only fair to assume other animals make the best possible use of their musculature as well.

Now I agree with creature, reducing a problem isn’t as good as not having the problem in the first place. But animal anatomy is not simply inferior overall, so having certain advantages tends to come with drawbacks, and reducing the drawbacks is what makes for an effective functional morphology.
Looking at a large theropod, perhaps it could not turn on the spot anywhere near as quickly as its quadrupedal prey, but how relevant is that? It still doesn’t really run the risk of its prey running circles around it unless the prey is also superior in other aspects of mobility, such as linear accelleration and speed (which is certainly not the case for a hippo compared to Carnotaurus).
Also, a theropod, without properly "turning" at all will, simply by means of flexing its body and neck have significant reach to the sides, so it doesn’t really need to turn all that quickly. You are save from being bitten by a hippo (at least for the moment) if you are standing 2 metres next to it, but an Allosaurus with the same body mass could probably snatch you right from where it is standing.

Now admittedly, Carnotaurus itself is probably not the best candidate for enhancing agility this way, since it had a rather stiff vertebral collumn (Méndez 2014) compared to some other theropods (it’s rather specialized for linear bursts of speed if you ask me). I don’t know how inflexible it was–certainly not a stiff rod, and certainly this would be relevant even with it, but probably less than with other theropods. Your best bet for terms of lateral flexibility among large theropods would likely be spinosaurs and allosaurs.

Also it’s strange that the hippo’s mobility hasn’t been called into question more. Yes, they can reach respectable speed by gallopping, but that’s recruiting the musculature of the torso too, which it can’t really use effectively to reduce torque, unlike the theropod. Assuming its legs are just as powerful as those of Carnotaurus seems to be a highly questionable assumption, so we’re not just talking "all else being equal" here, theropods, and Carnotaurus in particular, has crazy huge leg and tail muscles that will mean its accelleration in a straight line will likely be superior. That also means that Carnotaurus may not be able to generate as much torque, but the hippo is also limited in its turning performance, despite having an easier time rotating its body mass, namely by the speed at which its legs can step sideways. Carnotaurus needs more muscular effort to generate the same torque, but it probably has more, and having it, it can generate that torque more quickly.

––Ref:
Mazzetta, Gerardo V.; Fariña, Richard A.; Vizcaíno, Sergio F. (1998): On the Palaeobiology of the South American horned Theropod Carnotaurus sastrei Bonaparte. Gaia 15 pp. 185-192.
Méndez, Ariel H. (2014): The cervical vertebrae of the Late Cretaceous abelisaurid dinosaur Carnotaurus sastrei. Acta Palaeontologica Polonica 59 (3) pp. 569-579.

[Infinity Blade]

Thanks for the reply!

So then, do you think that a theropod may sometimes use an advantage in greater agility against quadrupedal opponents? That is, would a theropod have an advantage in agility to use against something like a hippo, rhino, or elephant? Or would simply turning to some degree (possibly while moving) and letting the flexibility of the neck and torso take care of the rest (to snag them in their jaws) be their way of dealing with them? How might you see a confrontation playing out?

[Infinity Blade]

Also, what would this mean for the night stalker rex thing? While I won't rule out the idea that Tyrannosaurus ever did it (because as noted, it would be an excellent way of exploiting any prey item in the ecosystem), would it really have been so unagile compared to its prey that it would have become an important reason to do it?

[theropod]

Depends on the theropod. If you mean at equal sizes, I don’t think a theropod would be more "agile", but it might have an advantage in some areas, which it would exploit, and a disadvantage in others, which it would try to compensate for. I don’t think a theropod could turn on the spot quite as well as an equal-sized quadruped (although I think for aforementioned reasons their turning ability tends to be underestimated), but I think in exchange it would potentially have an edge in linear accelleration, and as mentioned before it would not have to rely quite so much on turning ability in the first place in order to bring its assets to bear.
In fact, why would it even want to turn on the spot, unless it was afraid of being outflanked, which as I already explained is highly unlikely for reasons other than turning ability? I think we can agree that running circles around a prey item is fairly unlikely even with superb turning ability, so that’s not relevant either. Swift turns during chases maybe? Well, that’s indeed not something I’d envision large theropods to have been in the habit of doing, though of course their prey in such a scenario (the only large prey items that really spring to mind as flight animals would be ornithopods) has very much the same problem. As for juveniles or smaller theropods, I think they get exponentially better at turning, being not just smaller and leggier but having more slender bodies and lighter skulls and necks. So they are inherently more suitable for that, and I’m certainly not the first to hypothesize about the different ecomorphotypes a single theropod would have throughout ontogeny.

So would an adult T. rex run circles around a Triceratops the way lions can with buffalo? Certainly not. But could it out-accellerate it using its humungous leg muscles? That would seem realistic to me. So I think that certainly supports the nightstalker hypothesis, but also pretty much any conceivableambush scenario.

If you are referring to the Carnotaurus/hippo confrontation, I’ll have to venture somewhat off-topic:
Similar to what I argued before regarding rhinos, I think the mammals probable style of attack, attempting to charge at it open-mouthed as in an intraspecific rivalry would be fairly ineffective; a Carnotaurus could simply sidestep and at the same time attack its flank or leg without having to turn much at all. Even if it doesn’t, I’d see the hippo having some trouble doing severe damage because it’s angles of attack are limited on a taller opponent, and it would at the same time expose its back to a possibly more effective slashing attack from the abelisaur.
This goes for many large mammals (rhinos, hippos, elephants, bovids etc.). They are no pushovers when faced against the animals they coexist with, but ultimately none of them have ever had to face a predator in their own size range, meaning they aren’t adapted for it, neither behaviourally nor anatomically (elephants, due to their high cognitive capacities and long tusks, may fare better than the rest though). The only similar-sized opponents these megaherbivores ever have tend to be conspecifics, which are a very different thing (not necessarily trying to kill them for starters, but also anatomically not comparable to a giant theropod that it equipped to hunt large herbivores efficiently). In effect, they are a sauropod analogue, bigger than any potential predator and inherently reliant on their size and strength. That’s also why I tend to think thyreophorans, ceratopsids or suids would have considerably better odds against similar-sized predators, all these animals actually have such predators and have proven their ability to deal with them.

[Infinity Blade]

Okay, so let me see if I'm getting things straight. Theropods may not have really been more agile than their quadrupedal prey (even then, their turning ability was not as horrible as people make it out to be), but they could most likely accelerate more quickly than they could (on the basis of what specific anatomical features, though?) and this, in addition to the flexibility of their necks and torsos (which would grant them great reach), would obviate the need to turn quickly on the spot to bring their assets to bear (as these would have been their actual means of doing it).

When the dinosaur is linearly accelerating, is it moving parallel to its opponent in the opposite direction? If so, would it then turn its head, neck, and torso to snag its victim?

The talk about side-stepping sounds interesting. What anatomical characteristics would allow theropods to do this?

[theropod]

Sept 27, 2016 6:35:50 GMT 5 Infinity Blade said:

Okay, so let me see if I'm getting things straight. Theropods may not have really been more agile than their quadrupedal prey (even then, their turning ability was not as horrible as people make it out to be), but they could most likely accelerate more quickly than they could (on the basis of what specific anatomical features, though?)

What are perhaps the proportionately biggest leg muscles in the animal kingdom in some theropods, namely huge hip extensors (caudofemorales) and ilial muscle complexes.

When the dinosaur is linearly accelerating, is it moving parallel to its opponent in the opposite direction? If so, would it then turn its head, neck, and torso to snag its victim?

I didn’t mean both at once. If it were standing parallel to its opponent, yes, I’d envision it doing that (or many theropods at any rate). But accellerating at the same time is rather disadvantageous, it will want to keep the relative speed between itself and the prey item as low as possible, i.e. run alongside it at the same speed, or stand alongside it. If one is moving faster than the other that makes biting more difficult, although I do think (as e.g. in the hippo or rhino examples) that it’s still practical.
What I think high accelleration would be used for is overtaking its prey initially, especially from ambush.

The talk about side-stepping sounds interesting. What anatomical characteristics would allow theropods to do this?

Well, I might not really get the question. "Legs" would be the obvious answer. An animal with legs automatically has the capacity to sidestep at least to an extent, although how good it is depends on the flexibility and length of the legs in question. Now compared to many similar-sized animals theropods tend to have rather long legs (there are exceptions of course), so a single step to the side will take them comparatively far. Apart from that, the only more specific thing that springs to mind is the obtusely angled femoral neck of derived carcharodontosaurs, which could be an adaption for increased lateral flexibility of the hip joint (would make sense in animals that supposedly hunted sauropods). But whether this adaption is present or not, I’d generally assume theropods were capable of stepping to the side, especially since it’s another blatantly obvious method by which to avoid having to turn. As a side note, this is extremely speculative of course, maybe this could represent an evolutionary pressure to retain the ancestral laterally facing eyes and poor stereoscopic overlap in favour of good lateral vision.

[Infinity Blade]

Alright then.

I forgot that another important part of our discussion was the talk about pneumaticity. I think LionClaws thought that that would be disadvantageous for agility in theropods (I think he gives his reasoning in the discussion).

[theropod]

I think it’s possible that he doesn’t really understand how pneumaticity works and what its use is, but generally what he sais on that matter is true, just not relevant.
Yes, if a theropod somehow had all the air squeezed out of it anteroposteriorly as in his accordion-example, its RI would get lower. The result just wouldn’t be a viable organism though. It’s like saying "If we take this building and fill the space inside with concrete, it will be super-resistant to tornados!"–that’s true, but it won’t function in its intended role either. A theropod that has a slightly lower RI because it is a little shorter at the same mass, but has a weak bone structure, inferior bite and no respiratory system is no good either.

The pneumaticity in a theropod skeleton serves to lighten it while retaining its strength (or strengthen it while retaining its light weight, whichever you prefer). I think we can all agree that strength is a desirable quality for a skeleton.
If you took a theropod skull and filled all the airspaces with compact bone, it would be terribly heavy with the same shape and pretty much no gain in functionality (arguably a loss as far as quick slashes are concerned). If you took a theropod skull and shrunk it down so that at the same mass there was no air in it, it would be terribly small and definitely with reduced bite potency.

So in the end pneumatic spaces are helpful for agility. The parts that have the greatest impact on RI (head, neck, anterior torso) in particular are much lighter than an equally functional, non-pneumatized equivalent would be. And having this built is certainly better than having the same morphology but just removing the airspace. It’s also sort of stupid to only look at the total length and not at how the weight is distributed along that length imo. Being 10% longer but with the extremes having almost negligible weight (e.g. a light snout or tail tip) is better than being shorter but having a heavy, massive structure right on the end of that length.

In the end, of course all of this is "reducing the problem", but at least he can hardly complain about a lack of adaptions to do so, there is obviously an abundance of ways in which theropods were able to make up for their elongated body shape.

[Infinity Blade]

About the large mammal-sauropod analogy; just to be clear, the former would still be significantly less contingent on their size and strength than the latter would be due to possessing much better weaponry, right?

[theropod]

Typically I should think so, yes. In specific cases, it obviously depends on the mammal and the sauropod you are comparing…